# Problems on Profit Loss

Q31. By selling a table for Rs. 450 instead of Rs. 500 loss percent increases by 5%. The cost price of the table is

(a) Rs. 500

(b) Rs. 850

(c) Rs. 1000

(d) Rs. 1200

**Answer:** (c) Rs. 1000

Let the C.P be Rs. x

1st loss % = | (x - 500) | X 100 |

x |

= | 100 (x - 500) |

x |

2nd loss % = | x - 450 | X 100 |

x |

= | 100 (x - 450) |

x |

A/Q, | 100 (x - 450) | = | 100 (x - 500) | + 5 |

x | x |

⇒ | 100 (x - 450) | - | 100 (x - 500) | = 5 |

x | x |

⇒ | 100x - 45000 - 100x + 50000 | = 5 |

x |

⇒ 5x = 5000

⇒ x = Rs. 1000

Q32. A man buys an article for 5% less than its value and sells it for 5% more than its value. His gain or loss percent is

(a) 10(10/19)%

(b) 15(5/9)%

(c) 29(12/17)%

(d) 32(12/17)%

**Answer:** (a) 10(10/19)%

Let the value of the article be Rs. x

∴ C.P = Rs. (x X | 95 | ) = Rs. | 19x |

100 | 20 |

S.P = Rs. (x X | 105 | ) = Rs. | 21x |

100 | 20 |

∴ Gain % = Rs. ( | 21x | - | 19x | ) = Rs. | 2x | = Rs. | x |

20 | 20 | 20 | 10 |

∴ Gain % = | x/10 | X 100 |

(19/20)x |

= | x | X | 20 | X 100 |

10 | 19x |

= | 200 | % |

19 |

= 10 | 10 | % |

19 |

Q33. The marked price of an article is 5% more then the cost price and a discount of 5% is given on the marked price. Then the loss is

(a) 0.25%

(b) 0.65%

(c) 0.72%

(d) 0.99%

**Answer:** (a) 0.25%

Let the C.P be Rs. 100

∴ M.P = Rs. 105

∴ S.P = 95% of Rs. 105

= (95/100) X 105 = Rs. 99.75

∴ Loss = Rs. (100 - 99.75) = 0.25%

Q34. The marked price of a radio is Rs. 2000. The shopkeeper allows a discount of 10% and gain 8%. If no discount is allowed his gain percent would be

(a) 15%

(b) 20%

(c) 27%

(d) 33%

**Answer:** (b) 20%

S.P = 90% of Rs. 2000 = (90/100) X 2000 = Rs. 1800

Gain = 8%

∴ C.P = Rs. (100/108) X 1800 = Rs. 1666.66

New S.P = Rs. 2000

C.P = Rs. 1666.66

∴ Gain % = (333.34/1666.66) X 100 = 20%

Q35. A trader lists his articles 10% above the C.P and allows a discount 5% on cash payment. His gain percent is

(a) 3.7%

(b) 4.1%

(c) 4.5%

(d) 5.2%

**Answer:** (c) 4.5%

Let the C.P be Rs. 100

∴ M.P = Rs. 110

S.P = 95% of Rs. 110

= (95/100) X 110 = Rs. 104.50

∴ Gain = Rs. (104.50 - 100) = Rs. 4.50

Gain % = 4.5%

Q36. A dealer processing to sell his goods at cost price, uses 900 gm weight for 1kg. His gain percentage is

(a) 11(1/9)%

(b) 12(1/3)%

(c) 14(1/2)%

(d) 17(1/3)%

**Answer:** (a) 11(1/9)%

Gain % = { | Error | X 100} % |

True value - Error |

= { | 100 | X 100} % |

1000 - 100 |

= { | 100 | X 100} % |

900 |

= 11 | 1 | % |

9 |

Q37. The selling price of an article is ¾ times its cost price. The loss percent is

(a) 25%

(b) 34%

(c) 38%

(d) 39%

**Answer:** (a) 25%

Let the C.P be Rs. 100

∴ S.P = Rs. 100 X (3/4) = Rs. 75

∴ Loss % = 100 - 75 = 25%

Q38. The selling price of an article is 5/4 times its cost price. The gain percent is

(a) 25%

(b) 34%

(c) 38%

(d) 39%

**Answer:** (a) 25%

Let the C.P be Rs. 100

∴ S.P = Rs. 100 X (5/4) = Rs. 125

∴ Gain % = 125 - 100 = 25%

Q39. On selling an article for Rs. 56, one losses 20%. In order to gain 20% what would be the selling price

(a) Rs. 47

(b) Rs. 54

(c) Rs. 62

(d) Rs. 84

**Answer:** (d) Rs. 84

Let the C.P be Rs. x

∴ 80% of x = 56

⇒ (80/100) X x = 56

⇒ x = (560/8) = 70

∴ C.P = Rs. 70

Gain = 20%

∴ S.P = Rs. (120/100) X 70 = Rs. 84

Q40. By selling 33m of cloth Ram gained the cost price of 11m. The gain percent is

(a) 25(1/3)%

(b) 26(1/3)%

(c) 33(1/3)%

(d) 37(1/3)%

**Answer:** (c) 33(1/3)%

Let the C.P of 1m cloth be Rs. x

∴ The C.P of 33m cloth be Rs. 33x

Gain = 11x

∴ Gain % = (11x/33x) X 100

= 33(1/3)%